Prepare all of the ingredients.
In a slow cooker set to low, add broccoli, garlic, chicken, salt, pepper, onion, cream cheese chunks and chicken broth. Secure lid and let cook for 5½ hours.
Remove lid and stir to combine cheese into broth. Add parmesan cheese and heavy cream, stir to combine. Return lid and let cook for remaining 30 minutes.
Start water boiling for pasta. Once boiling, add pasta and cook as directed on package. Drain in colander, rinse with cool water to arrest cooking process and return to pot. Add melted butter and toss to evenly coat.
In a bowl, add a portion (about a cup) of pasta. Ladle soup over top until pasta is "floating". Garnish with parmesan and parsley, if desired.